On considère le problème de l'estimation de la densité et du terme de dérive par l'observation d'une trajectoire d'un processus de diffusion homogène en dimension d ayant une densité invariante unique. On construit les estimateurs par la méthode des noyaux, puis on en étudie le comportement asymptotique en et presque sûr. Finalement, on donne à titre d'exemple une classe de processus qui satisfont nos hypothèses.
We consider the problem of the density and drift estimation by the observation of a trajectory of an dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type and study the mean-square and almost sure uniform asymptotic behavior for these estimators. Finally, we give a class of processes satisfying our assumptions.
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@article{CRMATH_2007__345_2_101_0, author = {Bianchi, Annamaria}, title = {Nonparametric trend coefficient estimation for multidimensional diffusions}, journal = {Comptes Rendus. Math\'ematique}, pages = {101--105}, publisher = {Elsevier}, volume = {345}, number = {2}, year = {2007}, doi = {10.1016/j.crma.2007.05.012}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2007.05.012/} }
TY - JOUR AU - Bianchi, Annamaria TI - Nonparametric trend coefficient estimation for multidimensional diffusions JO - Comptes Rendus. Mathématique PY - 2007 SP - 101 EP - 105 VL - 345 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.05.012/ DO - 10.1016/j.crma.2007.05.012 LA - en ID - CRMATH_2007__345_2_101_0 ER -
%0 Journal Article %A Bianchi, Annamaria %T Nonparametric trend coefficient estimation for multidimensional diffusions %J Comptes Rendus. Mathématique %D 2007 %P 101-105 %V 345 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.05.012/ %R 10.1016/j.crma.2007.05.012 %G en %F CRMATH_2007__345_2_101_0
Bianchi, Annamaria. Nonparametric trend coefficient estimation for multidimensional diffusions. Comptes Rendus. Mathématique, Tome 345 (2007) no. 2, pp. 101-105. doi : 10.1016/j.crma.2007.05.012. http://www.numdam.org/articles/10.1016/j.crma.2007.05.012/
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